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3 years ago

7

The formula for the volume of a sphere is. What is the formula solved for r?

1 answer:

nataly862011 [7]3 years ago

3 0

Answer:

$r = \sqrt[3]{\dfrac{3V}{4 \pi}}$

Step-by-step explanation:

$V = \dfrac{4}{3}\pi r^3$

$\dfrac{4}{3}\pi r^3 = V$

$\pi r^3 = \dfrac{3V}{4}$

$r^3 = \dfrac{3V}{4 \pi}$

$r = \sqrt[3]{\dfrac{3V}{4 \pi}}$

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Which sequence is modeled by the graph below?

mariarad [96]

Answer:

$a_n=27\left(\dfrac{1}{3}\right)^{n-1}$

Step-by-step explanation:

From inspection of the graph, the given points are:

(2, 9)
(3, 3)
(4, 1)

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

<u>General form</u> of a geometric sequence:

$a_n=ar^{n-1}$

where:

a is the first term
r is the common ratio
$a_n$ is the nth term

Rewrite the given points as terms of the sequence:

(2, 9) ⇒ a₂ = 9
(3, 3) ⇒ a₃ = 3
(4, 1) ⇒ a₄ = 1

To find the common ratio r, divide consecutive terms:

$\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}$

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

$\implies a_2=9$

$\implies a\left(\dfrac{1}{3}\right)^{2-1}=9$

$\implies \dfrac{1}{3}a=9$

$\implies a=27$

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

$a_n=27\left(\dfrac{1}{3}\right)^{n-1}$

Learn more about geometric sequences here:

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5 0

1 year ago

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PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER!!

musickatia [10]

Answer:

$p>\frac{1}{14}$

Step-by-step explanation:

Question: $-31p+79>-59p+81$

1) Subtract 79 from both sides:

$-31p>-59p+2$

2) Add 59p to both sides:

$28p>2$

3) Divide both sides by 28:

$p>\frac{2}{28}$

4) Simplify fraction:

$p>\frac{1}{14}$

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3 years ago

Which of the following is a false statement? Solid substances need different temperature of heat to melt them. All solid substan

maria [59]

Answer:

All solid substances require the same temperature and heat to melt them.

Step-by-step explanation:

Depending on the substance, the required heat to melt it changes, and is not the same for every solid.

4 0

3 years ago

This is for today help pls!!!

ryzh [129]

Answer:

Perimeter=25 units

Area= 43 units^2

Step-by-step explanation:

one side = 5 units so perimeter is 5x5=25

split into 5 equal triangles

base =5, height =3.44, formula for area=(base)(height)(0.5)

area of each triangle =(5)(3.44)(0.5)=8.6

entire area=5(8.6)=43

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3 years ago

What is the measure of XYZ shown in the diagram below?

Crazy boy [7]

Answer: A.

Explenation: Apex

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3 years ago

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